Question

A piece of land is \[10.5\] m long and \[4.2\] m wide. Two square flower beds each \[1.2\] m wide are made in it and the rest id used for laying grass. What is the area of the grass portion of the field?

Answer 1

Hint: Find the area of the field by using formula for area of rectangle and find the area of the bed by using formula for area of square then subtract the area of both the squares from the area of the rectangle.

Complete step-by-step solution:
First, we will draw the figure to understand the question,

To obtain the area of the grass portion we have to subtract the area of flower beds from the area of land.
We are computing the area of land \[{A_l}\] by using the formula for area of rectangle \[A = l \cdot b\] where l is length and b is width.
Substituting \[l = 10.5\] and \[b = 4.2\] into \[A = l \cdot b\],
\[
  {A_l} = 10.5 \times 4.2 \\
   = 44.1{\text{ }}{{\text{m}}^2} \\
\]
Now we will compute the area of one bed by using the formula for area of square where a is the side of the square.
Substituting \[a = 1.2\] into \[A = {a^2}\],
\[
  {A_b} = 1.2 \times 1.2 \\
   = 1.44{\text{ }}{{\text{m}}^2} \\
\]
This is the area of one bed, multiplying \[{A_b}\] by two to find the area of both flower beds.
\[
  2{A_b} = 2 \times 1.44 \\
   = 2.88\,{{\text{m}}^2} \\
\]
Now, subtracting the area of both flower beds from the area of land,
\[
  {A_l} - 2{A_b} = 44.1 - 2.88 \\
   = 41.22{\text{ }}{{\text{m}}^2} \\
\]

Thus, the area of the grass portion of the field is \[41.22{\text{ }}{{\text{m}}^2}\].

Note:
In these types of questions find all the required areas, then subtract the smallest area from the largest area. The field has two square flower beds. Compute the area of one bed and multiply this area by two to get the area of both the beds.